A328813 Constant term in the expansion of (-1 + Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.

1, 1, 7, 115, 8071, 1770951, 1505946121, 4368457532265, 49949721645153751, 2021436054924485283799, 327902645022367779788597977, 191573267131797606250658812550565, 453516825886934673673734108656254582801

Offset: 0

Author

Seiichi Manyama, Oct 28 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..58

Crossrefs

Cf. A328747, A328812, A328814.

Programs

Mathematica

a[n_] := Sum[(-1)^(n-i) * Binomial[n, i] * Sum[Binomial[i, j]^(n+1), {j, 0, i}], {i, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, May 06 2021 *)

PARI

{a(n) = sum(i=0, n, (-1)^(n-i)*binomial(n, i)*sum(j=0, i, binomial(i, j)^(n+1)))}

Formula

a(n) = A328747(n,n+1) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^(n+1).